Average Error: 31.0 → 0.0
Time: 1.5s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r339638 = re;
        double r339639 = r339638 * r339638;
        double r339640 = im;
        double r339641 = r339640 * r339640;
        double r339642 = r339639 + r339641;
        double r339643 = sqrt(r339642);
        double r339644 = log(r339643);
        return r339644;
}
↓
double f(double re, double im) {
        double r339645 = re;
        double r339646 = im;
        double r339647 = hypot(r339645, r339646);
        double r339648 = log(r339647);
        return r339648;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.0

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))